The one-stop Mary Sue litmus test

It occurred to me that there exists one foolproof question for testing your character's attributes and determining whether you've got a dreaded Mary Sue (or Gary Stu): Why does my character have this attribute? If the answer is "Because it's cool!", your character is a Mary Sue.

Why does my character have red hair? Because I think red hair is so cool! MARY SUE.

Why does my character have a cool nickname like "Wizard" or "Ace"? Because it's cool! MARY SUE.

Why is my character strong and self-assured, entirely free of self-doubt or error? Because it's cool (and I sure wish I were like that)! MARY SUE.

BONUS CLINCHER QUESTION: Would it change the story at all if I did not specify that my character has these attributes? No. MARY SUE.

Don't thank me. Just don't write Mary Sues and Gary Stus. That will be thanks enough.